Question

if an ice cream shop has one flavor of ice cream,and 5 different toppings, how many combinations of different types of sundaes can you make

Answer 1

how do u define a sundae??

Answer 2

one flavor of ice cream (in this case it can only be vanilla) with X amount of toppings. ( a sundae with caramel nuts and whipped cream is the same thing as a sundae topped with whipped cream nuts and caramel)

Answer 3

i am not much into ice creams or permutations nd combinations :D

Answer 4

5+4+3+2+1

Answer 5

One way to think about this: Start with the ice cream (just the one flavor). Then for each of the five toppings you can either include it or not: yes or no, two possible choices. The total number of choices is then 2 x 2 x 2 x 2 x 2 = 32. Note that if you don't want to count the option of having no toppings at all then the total number of possible sundaes is 31.

Answer 6

32 is the number that I came up with as well, but that was just by trial and error. I am just not sure who to represent that with a formula.

Answer 7

*how not who

Answer 8

To add to my previous comment: This is an example of the general problem of taking a set of n things (in this case 5 toppings) and figuring out how many possible subsets of those things you can create. The answer is 2^n, that is 2 raised to the n-th power. So for one topping (say fudge sauce) you have two options (with fudge sauce or without) or 2^1, with two toppings (say fudge sauce and whipped cream) you have four options (nothing, fudge sauce only, whipped cream only, or both) or 2^2, and so on.

Answer 9

That is helpful. Thank you!